Least Common Multiple Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Least Common Multiple.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
The smallest positive integer that is divisible by each of two or more given numbers—where their multiples first coincide.
The first number that appears in both times tables—where two counting sequences land on the same value.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: LCM is the smallest number both can divide into evenly; use prime factorization, taking the largest power of each prime.
Common stuck point: Using prime factorization: LCM uses the larger power of each prime.
Sense of Study hint: List the first several multiples of each number side by side until you spot the first one that appears in both lists.
Worked Examples
Example 1
easySolution
- 1 Prime-factor each number: 12 = 2^2 \times 3 and 18 = 2 \times 3^2.
- 2 For the LCM, keep the highest exponent of each prime that appears: 2^2 and 3^2.
- 3 Multiply those factors: 2^2 \times 3^2 = 4 \times 9 = 36, so the LCM is 36.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
easyRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.